{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 一.算法推导\n",
    "Gibbs算法其实就是单分量MH算法中，建议分布取满条件概率分布的特殊情况，即：    \n",
    "\n",
    "$$\n",
    "q(x_j^{(i-1)}\\rightarrow x_j^{'(i)} \\mid x_{-j}^{(i)})=p(x_j^{'(i)} \\mid x_{-j}^{(i)})\n",
    "$$   \n",
    "\n",
    "那自然的，我们接下来还会关心接收概率$\\alpha(x_j^{(i-1)}\\rightarrow x_j^{'(i)}\\mid x_{-j}^{(i)})$的情况：   \n",
    "\n",
    "$$\n",
    "\\alpha(x_j^{(i-1)}\\rightarrow x_j^{'(i)}\\mid x_{-j}^{(i)})=min\\{1,\\frac{p(x_j^{'(i)}\\mid x_{-j}^{(i)})q(x_j^{'(i)}\\rightarrow x_j^{(i-1)}\\mid x_{-j}^{(i)})}{p(x_j^{(i-1)}\\mid x_{-j}^{(i)})q(x_j^{(i-1)}\\rightarrow x_j^{'(i)}\\mid x_{-j}^{(i)})}\\}=min\\{1,\\frac{p(x_j^{'(i)}\\mid x_{-j}^{(i)})p(x_j^{(i-1)}\\mid x_{-j}^{(i)})}{p(x_j^{(i-1)}\\mid x_{-j}^{(i)})p(x_j^{'(i)}\\mid x_{-j}^{(i)})}\\}=min\\{1,1\\}=1\n",
    "$$  \n",
    "\n",
    "接受率竟然始终为1，始终不会拒绝样本！所以Gibbs采样是一种特别高效的方法，下面直接说下采样流程"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  二.Gibbs采样流程\n",
    "输入：目标概率分布的密度函数$p(x)$，正整数$m,n,m<n$；   \n",
    "输出：$p(x)$的随机样本$x_{m+1},x_{m+2},...,x_n$\n",
    "\n",
    ">（1）初始化样本$x^{(0)}=(x_1^{(0)},x_2^{(0)},...,x_k^{(0)})$   \n",
    "\n",
    ">（2）对$i=1,2,...,m,m+1,...n$：   \n",
    "\n",
    ">>对$j=1,2,...,k$：   \n",
    "\n",
    ">>>根据建议分布$p(x_j\\mid x_{-j}^{(i)})$抽样第$j$维数据$x_j^{'(i)}$，并令$x_j^{(i)}=x_j^{'(i)}$   \n",
    "  \n",
    "\n",
    ">（3）返回样本集$\\{x_{m+1},x_{m+2},...,x_n\\}$  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 三.案例\n",
    "例子就用前一节的，直观感受一下与单分量MH的不同...公式部分就不码了..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "os.chdir('../')\n",
    "from ml_models import utils\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#定义均值，协方差\n",
    "u=np.asarray([0,0])\n",
    "sigma=np.asarray([[1,0.5],\n",
    "                  [0.5,1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import copy\n",
    "#采样的样本量\n",
    "nums=1000\n",
    "count=0\n",
    "points=[]\n",
    "#采样x0\n",
    "point=[np.random.randn(),np.random.randn()]\n",
    "points.append(point)\n",
    "while count<nums:\n",
    "    new_point=copy.deepcopy(point)\n",
    "    for k in (0,1):\n",
    "        # 按照满条件概率分布采样\n",
    "        new_point[k]=(np.random.randn()+0.5*new_point[(k+1)%2])*0.75\n",
    "    point=new_point\n",
    "    points.append(point)\n",
    "    count+=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\app\\Anaconda3\\lib\\site-packages\\matplotlib\\contour.py:967: UserWarning: The following kwargs were not used by contour: 'linewidth'\n",
      "  s)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x250f0cc8400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "utils.plot_contourf(np.asarray(points[-400:]),lambda x:utils.gaussian_nd(x,u,sigma),8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 四.小结\n",
    "对比一下Gibbs采样和单分量MH直接的异同点：   \n",
    "\n",
    "先说相同的地方：（1）两者都是要在满条件分布可用的前提下才能使用； （2）Gibbs采样是单分量MH的特殊情况，即建议分布取满条件概率分布的情况；    \n",
    "\n",
    "再说不同的地方：（1）满条件概率分布好采样时用Gibbs，不好采用时用单分量MH；（2）单分量MH有拒绝抽样的情况，而Gibbs采样全部接受   \n",
    "\n",
    "下面再补充一副关系图对抽样这一章的内容做总结   \n",
    "\n",
    "\n",
    "![avatar](./source/12_MCMC总结.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
